Path integral Monte Carlo approach to the structural properties and collective excitations of liquid $$$$^3{\text {He}}$$$$ without fixed nodes

Journal Article · Thu Jan 13 00:00:00 EST 2022 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-021-04355-9· OSTI ID:1839775

Dornheim, Tobias; Moldabekov, Zhandos A.; Vorberger, Jan; Militzer, Burkhard

Abstract Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic $$$$^4{\text {He}}$$$$ ${}^4\text{He}$ exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic $$$$^3{\text {He}}$$$$ ${}^3\text{He}$ is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid $$$$^3{\text {He}}$$$$ ${}^3\text{He}$ without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor $$$$S({\mathbf {q}})$$$$ $S\left(q\right)$ , the momentum distribution $$$$n({\mathbf {q}})$$$$ $n\left(q\right)$ , and the static density response function $$$$\chi ({\mathbf {q}})$$$$ $\chi \left(q\right)$ . In addition, the dynamic structure factor $$$$S({\mathbf {q}},\omega )$$$$ $S(q,\omega )$ is rigorously reconstructed from imaginary-time PIMC data. From simulations of $$$$^3{\text {He}}$$$$ ${}^3\text{He}$ , we derived the familiar phonon–maxon–roton dispersion function that is well-known for $$$$^4{\text {He}}$$$$ ${}^4\text{He}$ and has been reported previously for two-dimensional $$$$^3{\text {He}}$$$$ ${}^3\text{He}$ films (Nature 483:576–579 (2012)). The comparison of our new results for both $$$$S({\mathbf {q}})$$$$ $S\left(q\right)$ and $$$$S({\mathbf {q}},\omega )$$$$ $S(q,\omega )$ with neutron scattering measurements reveals an excellent agreement between theory and experiment.

• Research Organization: Univ. of California, Berkeley, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); Germany’s Federal Ministry of Education and Research (BMBF); Saxon Ministry for Science, Culture and Tourism (SMWK)
• Grant/Contract Number: SC0016248; NA0003842; shp00026
• OSTI ID: 1839775
• Alternate ID(s): OSTI ID: 1904861
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Vol. 12 Journal Issue: 1; ISSN 2045-2322
• Publisher: Nature Publishing Group
• Country of Publication: United Kingdom
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
atomic physics
molecular physics
chemical physics